GCSE Eduqas Music: Quick Reference Guide to Formulas & Theorems | GCSE Eduqas 音乐：公式定理速查手册

📚 GCSE Eduqas Music: Quick Reference Guide to Formulas & Theorems | GCSE Eduqas 音乐：公式定理速查手册

This handbook provides a compact collection of the most essential theoretical formulas, rules and theorems for GCSE Eduqas Music. From interval calculation to chord construction, from scale patterns to cadential formulas, every concept is presented in a clear, formulaic style that helps you revise quickly and apply knowledge confidently in listening, composing and performing tasks.

这本手册为 GCSE Eduqas 音乐课程汇集了最核心的理论公式、规则与定理。从音程计算到和弦构建，从音阶模式到终止式公式，每一个概念都以清晰的公式化风格呈现，帮助你在聆听、作曲和演奏评估中快速复习、自信运用。

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1. Intervals: Number & Quality | 音程：度数与性质

An interval is the distance between two pitches, defined by a number (2nd, 3rd, 4th, etc.) and a quality (major, minor, perfect, augmented, diminished). The number is counted from the lower note to the higher note using the letter names of the notes.

音程是两个音高之间的距离，由度数（二度、三度、四度等）和性质（大、小、纯、增、减）共同定义。度数是从较低音到较高音使用音名字母计算得出。

The quality of an interval depends on the exact number of semitones it contains. For perfect intervals (unison, 4th, 5th, octave) the base semitone counts are fixed: Perfect Unison = 0 semitones, Perfect 4th = 5 semitones, Perfect 5th = 7 semitones, Perfect Octave = 12 semitones.

音程的性质取决于其所包含的半音数量。纯音程（同度、四度、五度、八度）的基础半音数是固定的：纯一度 = 0 个半音，纯四度 = 5 个半音，纯五度 = 7 个半音，纯八度 = 12 个半音。

Major intervals (2nd, 3rd, 6th, 7th) serve as the reference for non-perfect intervals: Major 2nd = 2 semitones, Major 3rd = 4 semitones, Major 6th = 9 semitones, Major 7th = 11 semitones. If a major interval is reduced by one semitone it becomes minor; if increased by one semitone it becomes augmented.

大音程（二度、三度、六度、七度）是非纯音程的参照：大二度 = 2 个半音，大三度 = 4 个半音，大六度 = 9 个半音，大七度 = 11 个半音。大音程减少一个半音变为小音程，增加一个半音变为增音程。

Interval Formula: Major interval – 1 semitone = Minor; Perfect interval – 1 semitone = Diminished; Major or Perfect + 1 semitone = Augmented

音程公式：大音程 – 1 半音 = 小；纯音程 – 1 半音 = 减；大或纯 + 1 半音 = 增

Interval (音程)	Semitones (半音)	Example (示例)
Perfect Unison (纯一度)	0	C – C
Minor 2nd (小二度)	1	E – F
Major 2nd (大二度)	2	C – D
Minor 3rd (小三度)	3	A – C
Major 3rd (大三度)	4	C – E
Perfect 4th (纯四度)	5	G – C
Tritone (增四度/减五度)	6	C – F#
Perfect 5th (纯五度)	7	C – G
Minor 6th (小六度)	8	E – C
Major 6th (大六度)	9	C – A
Minor 7th (小七度)	10	G – F
Major 7th (大七度)	11	C – B
Perfect Octave (纯八度)	12	C – C’

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2. Scale Formulas | 音阶公式

A scale is a series of notes ordered by pitch, following a fixed pattern of tones (T, whole steps) and semitones (S, half steps). The major scale formula is the starting point for building many other scales.

音阶是一系列按音高排列的音符，遵循固定的全音（T）和半音（S）模式。大调音阶公式是构建许多其他音阶的起点。

Major Scale Formula: T – T – S – T – T – T – S

大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半

Natural minor scales use a different pattern of tones and semitones. Starting from the tonic, the natural minor scale is also known as the Aeolian mode.

自然小调音阶使用不同的全音与半音模式。从主音开始，自然小调也被称为爱奥里亚调式。

Natural Minor Scale Formula: T – S – T – T – S – T – T

自然小调音阶公式：全 – 半 – 全 – 全 – 半 – 全 – 全

The harmonic minor scale raises the 7th degree of the natural minor scale by a semitone, creating an augmented 2nd interval between the 6th and 7th degrees.

和声小调音阶将自然小调的第 VII 级升高半音，从而在第 VI 级与第 VII 级之间形成一个增二度音程。

Harmonic Minor Scale Formula: T – S – T – T – S – (T+S) – S

和声小调音阶公式：全 – 半 – 全 – 全 – 半 – （全+半） – 半

The melodic minor scale raises both the 6th and 7th degrees when ascending, and reverts to the natural minor form when descending.

旋律小调音阶在上行时升高第 VI 和第 VII 级，下行时回归自然小调形式。

Melodic Minor Ascending: T – S – T – T – T – T – S ; Descending: T – T – S – T – T – S – T (natural minor)

旋律小调上行：全 – 半 – 全 – 全 – 全 – 全 – 半；下行：全 – 全 – 半 – 全 – 全 – 半 – 全（自然小调）

Pentatonic scales omit two notes from the full seven-note scale, avoiding semitone steps. The major pentatonic scale uses scale degrees 1, 2, 3, 5, 6 of the major scale.

五声音阶省略七声调式中的两个音，避免了半音进行。大调五声音阶使用大调音阶的第 I、II、III、V、VI 级。

Major Pentatonic Formula: T – T – (T+S) – T – (T+S)

大调五声音阶公式：全 – 全 – （全+半） – 全 – （全+半）

Blues scales add a ‘blue’ note (flattened 5th) to the minor pentatonic, giving a characteristic expressive quality.

布鲁斯音阶在小调五声音阶基础上加入一个“蓝调”音（降 V 级），赋予其独特的表现力。

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3. Chord Construction | 和弦构成

A chord is built by stacking intervals, most commonly thirds. The basic triads are formed from a root, a third and a fifth. The type of triad (major, minor, diminished, augmented) is determined by the combination of intervals in semitones.

和弦通过叠加音程（最常见的三度）构成。基本三和弦由根音、三音和五音组成。三和弦的类型（大、小、减、增）由半音音程的组合决定。

Major Triad Formula: Root + 4 semitones (Major 3rd) + 3 semitones (Minor 3rd) → Root + 7 semitones (Perfect 5th)

大三和弦公式：根音 + 4 个半音（大三度） + 3 个半音（小三度） → 根音 + 7 个半音（纯五度）

Minor Triad Formula: Root + 3 semitones (Minor 3rd) + 4 semitones (Major 3rd) → Root + 7 semitones

小三和弦公式：根音 + 3 个半音（小三度） + 4 个半音（大三度） → 根音 + 7 个半音

Diminished Triad Formula: Root + 3 semitones + 3 semitones → Root + 6 semitones (Diminished 5th)

减三和弦公式：根音 + 3 个半音 + 3 个半音 → 根音 + 6 个半音（减五度）

Augmented Triad Formula: Root + 4 semitones + 4 semitones → Root + 8 semitones (Augmented 5th)

增三和弦公式：根音 + 4 个半音 + 4 个半音 → 根音 + 8 个半音（增五度）

Seventh chords add another third on top of the triad. The most common types in GCSE music are the dominant 7th and major 7th.

七和弦在三和弦上方再叠加一个三度。GCSE 音乐中最常见的类型是属七和弦和大七和弦。

Dominant 7th: Major triad + Minor 3rd → Root + 4 + 3 + 3 semitones (Root + 10 semitones)

属七和弦：大三和弦 + 小三度 → 根音 + 4 + 3 + 3 个半音（根音 + 10 个半音）

Major 7th: Major triad + Major 3rd → Root + 4 + 3 + 4 semitones (Root + 11 semitones)

大七和弦：大三和弦 + 大三度 → 根音 + 4 + 3 + 4 个半音（根音 + 11 个半音）

Chord inversions are determined by which chord member is in the bass. Root position = root in bass, first inversion = 3rd in bass, second inversion = 5th in bass, third inversion = 7th in bass (for seventh chords).

和弦转位由低音中的和弦音决定。原位 = 根音在低音，第一转位 = 三音在低音，第二转位 = 五音在低音，第三转位 = 七音在低音（对于七和弦）。

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4. Circle of Fifths & Key Signatures | 五度圈与调号

The circle of fifths arranges the 12 major and minor keys in a visual sequence of ascending perfect fifths. Moving clockwise adds sharps; moving anticlockwise adds flats. The relative minor is always a minor 3rd below its major key.

五度圈将 12 个大调和小调以上行纯五度的顺序排列。顺时针移动增加升号；逆时针移动增加降号。关系小调总是位于其大调下方小三度处。

Key Signature Formula for Sharps: The new sharp is the leading tone (7th degree) of the new major key. Order of sharps: F# C# G# D# A# E# B#

升号调号公式：新增的升号是新大调的导音（VII 级）。升号出现顺序：F# C# G# D# A# E# B#

Key Signature Formula for Flats: The new flat is the subdominant (4th degree) of the new major key. Order of flats: Bb Eb Ab Db Gb Cb Fb

降号调号公式：新增的降号是新大调的下属音（IV 级）。降号出现顺序：Bb Eb Ab Db Gb Cb Fb

To identify a major key from a sharp key signature, look at the last sharp and go up a semitone. For flat key signatures, the penultimate flat is the tonic.

要从升号调号识别大调，看最后一个升号并上行半音。对于降号调号，倒数第二个降号就是主音。

Major Key (大调)	Sharps/Flats (升/降号)	Relative Minor (关系小调)
C major	0	A minor
G major	1# (F#)	E minor
D major	2# (F#, C#)	B minor
A major	3# (F#, C#, G#)	F# minor
E major	4# (F#, C#, G#, D#)	C# minor
F major	1b (Bb)	D minor
Bb major	2b (Bb, Eb)	G minor

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5. Cadences | 终止式

A cadence is a pair of chords that close a musical phrase. Each cadence type has a distinctive harmonic formula, expressed here using Roman numerals.

终止式是结束乐句的一对和弦。每种终止式都有独特的和声公式，此处用罗马数字表示。

Perfect Cadence: V → I (full close, sounds finished)

完全终止：V → I（完全收束，听感结束）

Imperfect Cadence: I, II, IV or VI → V (half close, sounds unfinished)

不完全终止：I、II、IV 或 VI → V（半收束，听感未完成）

Plagal Cadence: IV → I (‘Amen’ cadence)

变格终止：IV → I（“阿门”终止）

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